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Boundary Value Problems 2013, 2013:72
doi:10.1186/1687-2770-2013-72

Published: 4 April 2013

Abstract

The aim of this work is to study adaptive fully-discrete finite element methods for
quadratic boundary optimal control problems governed by nonlinear parabolic equations.
We derive a posteriori error estimates for the state and control approximation. Such estimates can be used
to construct reliable adaptive finite element approximation for nonlinear quadratic
parabolic boundary optimal control problems. Finally, we present a numerical example
to show the theoretical results.